Place all ingredients except preserves, walnuts, and apricots into bread machine in the proper order for your machine. Use dough cycle. As the bread kneads, adjust the liquid to flour ratio if needed.
At the end of the dough cycle, remove dough and place on floured board. Cover and let rest for 10 minutes.
Roll out into a rectangle, brush with apricot preserves, and sprinkle walnuts and apricots on top. Roll up into a loaf, place in greased bread pan, cover, and let rise for 45 minutes.
At the end of the rising time, slash down the center, brush with a little beaten egg or egg substitute and milk, and bake in a preheated 375 degrees F (190 degrees C) oven for 25-30 minutes. Remove bread from pan, place on rack, and let cool.